A228563 E.g.f: A(x) = Sum_{n>=0} (1 + x*A(x)^n)^n * x^n/n!.

1, 1, 3, 13, 109, 1241, 18541, 340495, 7475721, 191215729, 5590994041, 184086712151, 6745657327069, 272484296020249, 12037353264295269, 577681783128081871, 29946086856245571601, 1668620115204908947937, 99516760157428436346481, 6329149392153729480812839

Offset: 0

Author

Paul D. Hanna, Aug 25 2013

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A143768.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,(1+x*A^k +x*O(x^n))^k*x^k/k!));n!*polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

Formula

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 109*x^4/4! + 1241*x^5/5! +...

where

A(x) = 1 + (1+x*A(x))*x + (1+x*A(x)^2)^2*x^2/2! + (1+x*A(x)^3)^3*x^3/3! + (1+x*A(x)^4)^4*x^4/4! + (1+x*A(x)^5)^5*x^5/5! +...